A186714 Triangular array C(n, k) = number of connected k-regular graphs, having girth at least 4, with n nodes, 0 <= k <= n div 2.

1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 6, 2, 1, 0, 0, 1, 0, 2, 0, 0, 0, 1, 22, 12, 1, 1, 0, 0, 1, 0, 31, 0, 0, 0, 0, 1, 110, 220, 7, 1, 1, 0, 0, 1, 0, 1606, 0, 1, 0, 0, 0, 1, 792, 16828, 388, 9, 1, 1, 0, 0, 1, 0, 193900, 0, 6, 0, 0, 0, 0, 1

Offset

1,23

Links

Table of n, a(n) for n=1..92.

Jason Kimberley, Connected regular graphs with girth at least 4

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

Example

01: 1;
02: 0,1;
03: 0,0;
04: 0,0,1;
05: 0,0,1;
06: 0,0,1,1;
07: 0,0,1,0;
08: 0,0,1,2,1;
09: 0,0,1,0,0;
10: 0,0,1,6,2,1;
11: 0,0,1,0,2,0;
12: 0,0,1,22,12,1,1;
13: 0,0,1,0,31,0,0;
14: 0,0,1,110,220,7,1,1;
15: 0,0,1,0,1606,0,1,0;
16: 0,0,1,792,16828,388,9,1,1;
17: 0,0,1,0,193900,0,6,0,0;
18: 0,0,1,7805,2452818,406824,267,8,1,1;
19: 0,0,1,0,32670330,0,3727,0,0,0;
20: 0,0,1,97546,456028474,1125022325,483012,741,13,1,1;
21: 0,0,1,0,6636066099,0,69823723,0,1,0,0;
22: 0,0,1,1435720,100135577747,3813549359274,14836130862,2887493,?,14,1,1;
23: 0,0,1,0,1582718912968,0,?,0,?,0,0;

Crossrefs

The sum of the n-th row is A186724(n).

Connected k-regular simple graphs with girth at least 4: A186724 (any k), this sequence (triangle); specified degree k: A185114 (k=2), A014371 (k=3), A033886 (k=4), A058275 (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).

Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth *at least* g: A068934 (g=3), this sequence (g=4), A186715 (g=5), A186716 (g=6), A186717 (g=7), A186718 (g=8), A186719 (g=9).

Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth *exactly* g: A186733 (g=3), A186734 (g=4).

Sequence in context: A319080 A025435 A304685 * A160382 A336352 A081221

Adjacent sequences: A186711 A186712 A186713 * A186715 A186716 A186717

Keyword

nonn,tabf,hard

Author

Jason Kimberley, Sep to Dec 2011.

Status

approved